College Algebra Essentials

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The&Eighth Edition of this highly dependable book retains its best featuresaccuracy, precision, depth, and abundant exercise setswhile substantially updating its content and pedagogy. Striving to teach mathematics as a way of life, Sullivan provides understandable, realistic applications that are consistent with the abilities of most readers. Chapter topics include Graphs; Polynomial and Rational Functions; Conics; Systems of Equations and Inequalities; Exponential and Logarithmic Functions; Counting and Probability; and more. For individuals with an interest in learning algebra as it applies to their everyday lives.

The Essentials Edition

xi

Preface to the Instructor

xiii

List of Applications

xix

Photo Credits

xxiii

Review

1

(82)

Real Numbers

2

(15)

Algebra Review

17

(12)

Geometry Review

29

(6)

Polynomials

35

(8)

Factoring Polynomials

43

(9)

Polynomial Division; Synthetic Division

52

(6)

Rational Expressions

58

(12)

nth Roots; Rational Exponents

70

(13)

Chapter Review

77

(6)

Equations and Inequalities

83

(74)

Linear Equations

84

(12)

Quadratic Equations

96

(13)

Quadratic Equations in the Complex Number System

109

(9)

Radical Equations; Equations Quadratic in Form; Factorable Equations

118

(7)

Solving Inequalities

125

(11)

Equations and Inequalities Involving Absolute Value

136

(5)

Applications: Interest, Mixture, Uniform Motion, Constant Rate Jobs

141

(16)

Chapter Review

151

(4)

Chapter Projects

155

(2)

Graphs

157

(60)

Rectangular Coordinates

158

(7)

Graphs of Equations

165

(10)

Circles

175

(6)

Lines

181

(13)

Parallel and Perpendicular Lines

194

(5)

Scatter Diagrams; Linear Curve Fitting

199

(7)

Variation

206

(11)

Chapter Review

212

(4)

Chapter Projects

216

(1)

Cumulative Review

216

(1)

Functions and Their Graphs

217

(74)

Functions

218

(13)

The Graph of a Function

231

(9)

Properties of Functions

240

(11)

Library of Functions; Piecewise-defined Functions

251

(11)

Graphing Techniques: Transformations

262

(13)

Mathematical Models: Constructing Functions

275

(16)

Chapter Review

283

(6)

Chapter Projects

289

(1)

Cumulative Review

290

(1)

Polynomial and Rational Functions

291

(100)

Quadratic Functions and Models

292

(20)

Polynomial Functions

312

(18)

Rational Functions I

330

(11)

Rational Functions II: Analyzing Graphs

341

(15)

Polynomial and Rational Inequalities

356

(6)

The Real Zeros of a Polynomial Function

362

(15)

Complex Zeros; Fundamental Theorem of Algebra

377

(14)

Chapter Review

383

(5)

Chapter Projects

388

(1)

Cumulative Review

389

(2)

Exponential and Logarithmic Functions

391

(100)

Composite Functions

392

(7)

Inverse Functions

399

(13)

Exponential Functions

412

(16)

Logarithmic Functions

428

(13)

Properties of Logarithms

441

(9)

Logarithmic and Exponential Equations

450

(5)

Compound Interest

455

(10)

Exponential Growth and Decay; Newton's Law; Logistic Models

465

(9)

Fitting Data to Exponential, Logarithmic, and Logistic Functions

474

(17)

Chapter Review

482

(6)

Chapter Projects

488

(1)

Cumulative Review

489

(2)

Analytic Geometry

491

(2)

Conics

The Parabola

The Ellipse

The Hyperbola

Chapter Review

Chapter Projects

Cumulative Review

Systems of Equations and Inequalities

493

(18)

Systems of Linear Equations: Substitution and Elimination

494

(17)

Systems of Linear Equations: Matrices

Systems of Linear Equations: Determinants

Matrix Algebra

Partial Fraction Decomposition

Systems of Nonlinear Equations

Systems of Inequalities

Linear Programming

Chapter Review

Chapter Projects

Cumulative Review

Sequences; Induction; the Binomial Theorem

511

(30)

Sequences

512

(9)

Arithmetic Sequences

521

(6)

Geometric Sequences; Geometric Series

527

(14)

Mathematical Induction

The Binomial Theorem

Chapter Review

Chapter Projects

Cumulative Review

Counting and Probability

541

(2)

Sets and Counting

Permutations and Combinations

Probability

Chapter Review

Chapter Projects

Cumulative Review

Appendix Graphing Utilities

543

1 The Viewing Rectangle

543

(2)

2 Using a Graphing Utility to Graph Equations

545

(4)

3 Using a Graphing Utility to Locate Intercepts and Check for Symmetry